Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
H. Bacry, "The de Sitter group and the bound states of the hydrogen atom", Nuovo Cimento, Vol. 41 (1966), 222–234.
J. Chazarain, "Formule de Poisson pour les variétés riemanniennes", Invent. Math. 24 (1974), 65–82.
Y. Colin de Verdiére, "Spectre du laplacien et longueurs des geodesiques periodiques", Comp. Math. 27 (1974), 159–184.
Y. Colin de Verdiére, "Sur le spectre des operateurs elliptiques a bicharacteristiques toutes periodiques", Commentarii Math. Helvetici 54 (1979), 508–522.
J. J. Duistermaat and V. Guillemin, "The spectrum of positive elliptic operators and periodic geodesics", Invent. Math. 29 (1975), 184–269.
W. Helton, "An operator-theoretic approach to partial differential equations, propagation of singularities and spectral theory", Indiana U. Math. Journ. Vol. 26, no. 6 (1977), 997–1018.
L. Hörmander, "The spectral function of an elliptic operator", Acta Math. 121 (1968), 193–218.
M. Kashiwara and M. Vergne, "Functions on the Shilov boundary of the generalized half-plane", in Non-commutative Harmonic Analysis, Lecture Notes in Math., No. 728, Springer, New York (1979).
B. Kostant, "Quantization and unitary representations", in Lectures in Modern Analysis and Applications, Springer Lecture Notes No. 170 (1970), 87–208.
B. Kostant, "Symplectic Spinors", Conv. di Geom. Simp. e Fis. Math., INDAM Rome (1973).
J. Moser, "Regularization of Kepler's problem and the averaging method on a manifold", Comm. Pure Appl. Math. 23 (1970), 609–636.
E. Onofri, "Dynamical quantization of the Kepler manifold", Istituto di Fisica, Parma (1965).
D. Shale, "Linear symmetries of free boson fields", Trams. Amer. Math. Soc. 103 (1962), 149–167.
M. A. Shubin and V. N. Tulovskii, "On asymptotic distribution of eigenvalues of pseudodifferential operators on IRn", Math. USSR Sbornik, 21 (1973), 565–583.
E. C. Titchmarsh, Eigenfunction Expansions Associated with Second-order Differential Equations Part II, Clarendon Press, Oxford (1958).
N. Wallach, Symplectic Geometry and Fourier Analysis, Math. Sci. Press, 53 Jordan Road, Brookline, Mass. (1977).
A. Weil, "Sur certaines groupes d'operateurs unitaires", Acta Math. 111 (1964), 143–211.
A. Weinstein, "Asymptotics of eigenvalue clusters for the Laplacian plus a potential", Duke Math. Journal 44 (1977), 883–892.
H. Widom, "Eigenvalue distribution theorems in certain homogeneous spaces", Journal of Functional Analysis, (to appear).
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1980 Springer-Verlag
About this paper
Cite this paper
Guillemin, V., Sternberg, S. (1980). The metaplectic representation, weyl operators and spectral theory. In: GarcÃa, P.L., Pérez-Rendón, A., Souriau, J.M. (eds) Differential Geometrical Methods in Mathematical Physics. Lecture Notes in Mathematics, vol 836. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0089755
Download citation
DOI: https://doi.org/10.1007/BFb0089755
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-10275-5
Online ISBN: 978-3-540-38405-2
eBook Packages: Springer Book Archive